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Journal articles on the topic 'Hodge classe'

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Published: 9 March 2023

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1

Fargues, Laurent. "G-torseurs en théorie de Hodge p-adique." Compositio Mathematica 156, no. 10 (October 2020): 2076–110. http://dx.doi.org/10.1112/s0010437x20007423.

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RésuméÉtant donné un groupe réductif $G$ sur une extension de degré fini de $\mathbb {Q}_p$ on classifie les $G$-fibrés sur la courbe introduite dans Fargues and Fontaine [Courbes et fibrés vectoriels en théorie de Hodge$p$-adique, Astérisque 406 (2018)]. Le résultat est interprété en termes de l'ensemble $B(G)$ de Kottwitz. On calcule également la cohomologie étale de la courbe à coefficients de torsion en lien avec la théorie du corps de classe local.

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2

Santiago, Gabrielli Stefaninni, Laura Ribeiro, Irene Da Silva Coelho, Miliane Moreira Soares de Souza, and Shana De Mattos de Oliveira Coelho. "TESTE DE HODGE MODIFICADO EM ÁGAR CLED PARA TRIAGEM DE Proteus mirabilis PRODUTORES DE CARBAPENEMASE." Revista Univap 24, no. 46 (December 17, 2018): 1. http://dx.doi.org/10.18066/revistaunivap.v24i46.397.

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Enterobacteriaceae produtoras de carbapenemase vêm sendo descritas em todo o mundo. Uma detecção precisa de bactérias produtoras de carpabenemase é necessária pois esta classe de antibióticos é usada no tratamento de infecções severas. A nível laboratorial, o método fenotípico para a detecção de produtores de carbapenemase é o teste de Hodge modificado. Entretanto, algumas enterobactérias tem grande motilidade dificultando a leitura e interpretação dos resultados desta técnica. O objetivo deste estudo foi validar um meio para se obter resultados confiáveis em bactérias com grande motilidade, como é o caso de Proteus mirabilis. O meio ágar Müller-Hinton, preconizado pelo CLSI, foi comparado ao ágar CLED que demostrou ser um bom meio para análise da produção de carbapenemase em Proteus mirabilis suspeitos de produzirem esta enzima embora todos os isolados tenham sido negativos no teste.

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3

Voisin, Claire. "Hodge loci and absolute Hodge classes." Compositio Mathematica 143, no. 04 (July 2007): 945–58. http://dx.doi.org/10.1112/s0010437x07002837.

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4

Mongardi, Giovanni, and John Christian Ottem. "Curve classes on irreducible holomorphic symplectic varieties." Communications in Contemporary Mathematics 22, no. 07 (November 15, 2019): 1950078. http://dx.doi.org/10.1142/s0219199719500780.

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We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of [Formula: see text]-type and of generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.

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5

van Geemen, B., and A. Verra. "Quaternionic pryms and Hodge classes." Topology 42, no. 1 (January 2003): 35–53. http://dx.doi.org/10.1016/s0040-9383(02)00004-6.

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6

Koike, Kenji. "Algebraicity of some Weil Hodge Classes." Canadian Mathematical Bulletin 47, no. 4 (December 1, 2004): 566–72. http://dx.doi.org/10.4153/cmb-2004-055-x.

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AbstractWe show that the Prym map for 4-th cyclic étale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.

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7

Cattani, Eduardo, Pierre Deligne, and Aroldo Kaplan. "On the locus of Hodge classes." Journal of the American Mathematical Society 8, no. 2 (May 1, 1995): 483. http://dx.doi.org/10.1090/s0894-0347-1995-1273413-2.

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8

Méo, Michel. "Chow forms and Hodge cohomology classes." Comptes Rendus Mathematique 352, no. 4 (April 2014): 339–43. http://dx.doi.org/10.1016/j.crma.2014.01.012.

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9

J. Moonen, B. J., and Yu G. Zarhin. "Hodge classes and Tate classes on simple abelian fourfolds." Duke Mathematical Journal 77, no. 3 (March 1995): 553–81. http://dx.doi.org/10.1215/s0012-7094-95-07717-5.

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10

Scavia, Federico. "Motivic classes and the integral Hodge Question." Comptes Rendus. Mathématique 359, no. 3 (April 20, 2021): 305–11. http://dx.doi.org/10.5802/crmath.178.

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11

Brosnan, Patrick, Gregory Pearlstein, and Christian Schnell. "The locus of Hodge classes in an admissible variation of mixed Hodge structure." Comptes Rendus Mathematique 348, no. 11-12 (June 2010): 657–60. http://dx.doi.org/10.1016/j.crma.2010.04.002.

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12

BRASSELET, JEAN-PAUL, JÖRG SCHÜRMANN, and SHOJI YOKURA. "HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES." Journal of Topology and Analysis 02, no. 01 (March 2010): 1–55. http://dx.doi.org/10.1142/s1793525310000239.

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In this paper we study some new theories of characteristic homology classes of singular complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class transformationmCy: K0( var /X) → G0(X) ⊗ ℤ[y], which generalizes the total λ-class λy(T*X) of the cotangent bundle to singular spaces. Here K0( var /X) is the relative Grothendieck group of complex algebraic varieties over X as introduced and studied by Looijenga and Bittner in relation to motivic integration, and G0(X) is the Grothendieck group of coherent sheaves of [Formula: see text]-modules. A first construction of mCy is based on resolution of singularities and a suitable "blow-up" relation, following the work of Du Bois, Guillén, Navarro Aznar, Looijenga and Bittner. A second more functorial construction of mCy is based on some results from the theory of algebraic mixed Hodge modules due to M. Saito. We define a natural transformation Ty* : K0( var /X) → H*(X) ⊗ ℚ[y] commuting with proper pushdown, which generalizes the corresponding Hirzebruch characteristic. Ty* is a homology class version of the motivic measure corresponding to a suitable specialization of the well-known Hodge polynomial. This transformation unifies the Chern class transformation of MacPherson and Schwartz (for y = -1), the Todd class transformation in the singular Riemann-Roch theorem of Baum–Fulton–MacPherson (for y = 0) and the L-class transformation of Cappell-Shaneson (for y = 1). We also explain the relation among the "stringy version" of our characteristic classes, the elliptic class of Borisov–Libgober and the stringy Chern classes of Aluffi and De Fernex–Lupercio–Nevins–Uribe. All our results can be extended to varieties over a base field k of characteristic 0.

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13

Srinivas, V. "Gysin maps and cycle classes for Hodge cohomology." Proceedings Mathematical Sciences 103, no. 3 (December 1993): 209–47. http://dx.doi.org/10.1007/bf02866988.

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14

Moonen, B. J. J., and Yu G. Zarhin. "Hodge classes on abelian varieties of low dimension." Mathematische Annalen 315, no. 4 (December 1, 1999): 711–33. http://dx.doi.org/10.1007/s002080050333.

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15

Looijenga, Eduard. "Goresky–Pardon lifts of Chern classes and associated Tate extensions." Compositio Mathematica 153, no. 7 (May 3, 2017): 1349–71. http://dx.doi.org/10.1112/s0010437x17007175.

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Let $X$ be an irreducible complex-analytic variety, ${\mathcal{S}}$ a stratification of $X$ and ${\mathcal{F}}$ a holomorphic vector bundle on the open stratum ${X\unicode[STIX]{x0030A}}$. We give geometric conditions on ${\mathcal{S}}$ and ${\mathcal{F}}$ that produce a natural lift of the Chern class $\operatorname{c}_{k}({\mathcal{F}})\in H^{2k}({X\unicode[STIX]{x0030A}};\mathbb{C})$ to $H^{2k}(X;\mathbb{C})$, which, in the algebraic setting, is of Hodge level ${\geqslant}k$. When applied to the Baily–Borel compactification $X$ of a locally symmetric variety ${X\unicode[STIX]{x0030A}}$ and an automorphic vector bundle ${\mathcal{F}}$ on ${X\unicode[STIX]{x0030A}}$, this refines a theorem of Goresky–Pardon. In passing we define a class of simplicial resolutions of the Baily–Borel compactification that can be used to define its mixed Hodge structure. We use this to show that the stable cohomology of the Satake ($=$ Baily–Borel) compactification of ${\mathcal{A}}_{g}$ contains nontrivial Tate extensions.

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16

Li, Zhiyuan, and Zhiyu Tian. "Integral Hodge classes on fourfolds fibered by quadric bundles." Proceedings of the American Mathematical Society 144, no. 8 (March 17, 2016): 3333–45. http://dx.doi.org/10.1090/proc/12999.

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17

Charney, Ruth, and Ronnie Lee. "Characteristic classes for the classifying spaces of hodge structures." K-Theory 1, no. 3 (May 1987): 237–70. http://dx.doi.org/10.1007/bf00533824.

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18

Blottière, David. "Réalisation de Hodge du polylogarithme d'un schéma abélien." Journal of the Institute of Mathematics of Jussieu 8, no. 1 (November 20, 2008): 1–38. http://dx.doi.org/10.1017/s1474748008000315.

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RésuméDans cet article, on démontre que les courants polylogarithmiques introduits par Andrey Levin décrivent le polylogarithme d'un schéma abélien au niveau topologique. De ce résultat, qu'Andrey Levin avait lui-même conjecturé, on déduit une méthode pour déterminer explicitement les classes d'Eisenstein des schémas abéliens au niveau topologique. Ces classes ont un intérêt particulier, car, comme Guido Kings l'a établi, elles ont une origine motivique. Dans une suite à ce travail intitulée «Les classes d'Eisenstein des variétés de Hilbert–Blumenthal», on utilise les résultats obtenus dans le présent article pour démontrer que les classes d'Eisenstein des variétés de Hilbert–Blumenthal dégénèrent au bord de la compactification de Baily–Borel de la base en une valeur spéciale de fonctionLassociée au corps de nombres totalement réel sous-jacent, et on en déduit, dans ce contexte géométrique, un résultat de non annulation pour certaines classes d'Eisenstein.

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19

Gros, Michel. "Classes de Chern et classes de cycles en cohomologie de Hodge-Witt logarithmique." Mémoires de la Société mathématique de France 1 (1985): 1–87. http://dx.doi.org/10.24033/msmf.322.

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20

Logares, Marina, and Vicente Muñoz. "Hodge polynomials of the SL(2, ℂ)-character variety of an elliptic curve with two marked points." International Journal of Mathematics 25, no. 14 (December 2014): 1450125. http://dx.doi.org/10.1142/s0129167x14501250.

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We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2, ℂ). When we fix the conjugacy classes of the representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons.

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21

Getzler, E., and R. Pandharipande. "Virasoro constraints and the Chern classes of the Hodge bundle." Nuclear Physics B 530, no. 3 (October 1998): 701–14. http://dx.doi.org/10.1016/s0550-3213(98)00517-3.

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22

Basok, Mikhail. "Discriminant and Hodge classes on the space of Hitchin covers." Letters in Mathematical Physics 110, no. 10 (June 27, 2020): 2659–74. http://dx.doi.org/10.1007/s11005-020-01303-y.

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23

Florentino, Carlos, and Jaime Silva. "Hodge-Deligne polynomials of character varieties of free abelian groups." Open Mathematics 19, no. 1 (January 1, 2021): 338–62. http://dx.doi.org/10.1515/math-2021-0038.

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Abstract Let F F be a finite group and X X be a complex quasi-projective F F -variety. For r ∈ N r\in {\mathbb{N}} , we consider the mixed Hodge-Deligne polynomials of quotients X r / F {X}^{r}\hspace{-0.15em}\text{/}\hspace{-0.08em}F , where F F acts diagonally, and compute them for certain classes of varieties X X with simple mixed Hodge structures (MHSs). A particularly interesting case is when X X is the maximal torus of an affine reductive group G G , and F F is its Weyl group. As an application, we obtain explicit formulas for the Hodge-Deligne and E E -polynomials of (the distinguished component of) G G -character varieties of free abelian groups. In the cases G = G L ( n , C ) G=GL\left(n,{\mathbb{C}}\hspace{-0.1em}) and S L ( n , C ) SL\left(n,{\mathbb{C}}\hspace{-0.1em}) , we get even more concrete expressions for these polynomials, using the combinatorics of partitions.

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24

Diwakar, Jyoti, Rajesh K. Verma, Dharmendra P. Singh, Amit Singh, and Sunita Kumari. "Phenotypic detection of carbapenem resistance in gram negative bacilli from various clinical specimens of a tertiary care hospital in Western Uttar Pradesh." International Journal of Research in Medical Sciences 5, no. 8 (July 26, 2017): 3511. http://dx.doi.org/10.18203/2320-6012.ijrms20173552.

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Background: Carbapenemase producing multidrug-resistant organisms (i.e., MDROs) is a critical medical and public health issue globally. These bacteria are often resistant to all beta-lactam agents and are also co-resistant to other multiple classes of antimicrobial agents, leaving very few antimicrobial options.Methods: This study was carried out at UP University of medical sciences Saifai, Etawah, Uttar Pradesh, India, from January 2015 to June 2016. 110 isolates were found resistant by the Kirby Bauer’s disc diffusion method according to the CLSI guidelines. Modified Hodge test and combined disk test were performed for resistant isolates.Results: A total of 800-gram negative isolate were included in the study. 110 isolates were found resistant to imipenem by disk diffusion method. Out of these 90 (81.81%) were positive for carbapenemase production by modified Hodge test.Conclusions: We conclude that the modified Hodge test is a useful method for detection of carbapenemase production. Combined disc method is useful to detect metallo beta lactamase production.

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25

Voisin, Claire. "Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal." Journal of Algebraic Geometry 22, no. 1 (May 23, 2012): 141–74. http://dx.doi.org/10.1090/s1056-3911-2012-00597-9.

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26

Méo, Michel. "Une propriété de continuité associée aux classes de cohomologie de Hodge." Comptes Rendus Mathematique 356, no. 7 (July 2018): 737–46. http://dx.doi.org/10.1016/j.crma.2018.05.008.

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27

MAICAN, MARIO. "THE HOMOLOGY GROUPS OF CERTAIN MODULI SPACES OF PLANE SHEAVES." International Journal of Mathematics 24, no. 12 (November 2013): 1350098. http://dx.doi.org/10.1142/s0129167x13500985.

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Using the Białynicki-Birula method, we determine the additive structure of the integral homology groups of the moduli spaces of semi-stable sheaves on the projective plane having rank and Chern classes (5, 1, 4), (7, 2, 6), respectively, (0, 5, 19). We compute the Hodge numbers of these moduli spaces.

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28

Dang, Nguyen-Bac, and Charles Favre. "Intersection theory of nef b-divisor classes." Compositio Mathematica 158, no. 7 (July 2022): 1563–94. http://dx.doi.org/10.1112/s0010437x22007515.

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We prove that any nef $b$ -divisor class on a projective variety defined over an algebraically closed field of characteristic zero is a decreasing limit of nef Cartier classes. Building on this technical result, we construct an intersection theory of nef $b$ -divisors, and prove several variants of the Hodge index theorem inspired by the work of Dinh and Sibony. We show that any big and basepoint-free curve class is a power of a nef $b$ -divisor, and relate this statement to the Zariski decomposition of curves classes introduced by Lehmann and Xiao. Our construction allows us to relate various Banach spaces contained in the space of $b$ -divisors which were defined in our previous work.

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29

Buskin, Nikolay. "Every rational Hodge isometry between two K⁢3K3 surfaces is algebraic." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 755 (October 1, 2019): 127–50. http://dx.doi.org/10.1515/crelle-2017-0027.

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AbstractWe present a proof that for any Hodge isometry {\psi\colon\hskip-0.853583ptH^{2}(S_{1},{\mathbb{Q}})\hskip-0.853583pt% \rightarrow\hskip-1.13811ptH^{2}(S_{2},{\mathbb{Q}})} between any two Kähler {K3} surfaces {S_{1}} and {S_{2}} we can find a finite sequence of K3 surfaces and analytic (2,2)-classes supported on successive products, such that the isometry ψ is the convolution of these classes. The proof of this fact implies that for projective {S_{1},S_{2}} the class of ψ is algebraic. This proves a conjecture of I. Shafarevich [26].

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30

Bajpai, Jitendra, and Matias V. Moya Giusti. "Ghost classes in $${\mathbb {Q}}$$-rank two orthogonal Shimura varieties." Mathematische Zeitschrift 296, no. 3-4 (February 4, 2020): 1209–33. http://dx.doi.org/10.1007/s00209-020-02460-5.

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Abstract In this article, the existence of ghost classes for the Shimura varieties associated to algebraic groups of orthogonal similitudes of signature (2, n) is investigated. We make use of the study of the weights in the mixed Hodge structures associated to the corresponding cohomology spaces and results on the Eisenstein cohomology of the algebraic group of orthogonal similitudes of signature $$(1, n-1)$$ ( 1 , n - 1 ) . For the values of $$n = 4, 5$$ n = 4 , 5 we prove the non-existence of ghost classes for most of the irreducible representations (including most of those with an irregular highest weight). For the rest of the cases, we prove strong restrictions on the possible weights in the space of ghost classes and, in particular, we show that they satisfy the weak middle weight property.

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31

Buchdahl, Nicholas, and Georg Schumacher. "Polystable bundles and representations of their automorphisms." Complex Manifolds 9, no. 1 (January 1, 2022): 78–113. http://dx.doi.org/10.1515/coma-2021-0131.

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Abstract Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a neighbourhood of a given polystable bundle on a compact Kähler manifold are shown to be (poly)stable if and only if their corresponding classes are (poly)stable in the sense of geometric invariant theory with respect to the linear action of the automorphism group of the bundle on its space of in˝nitesimal deformations.

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Bauer, Ingrid, and Siegmund Kosarew. "On the Hodge spectral sequence for some classes of non-complete algebraic manifolds." Mathematische Annalen 284, no. 4 (December 1989): 577–93. http://dx.doi.org/10.1007/bf01443352.

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33

MARKMAN, EYAL. "INTEGRAL CONSTRAINTS ON THE MONODROMY GROUP OF THE HYPERKÄHLER RESOLUTION OF A SYMMETRIC PRODUCT OF A K3 SURFACE." International Journal of Mathematics 21, no. 02 (February 2010): 169–223. http://dx.doi.org/10.1142/s0129167x10005957.

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Let S[n]be the Hilbert scheme of length n subschemes of a K3 surface S. H2(S[n],ℤ) is endowed with the Beauville–Bogomolov bilinear form. Denote by Mon the subgroup of GL [H*(S[n],ℤ)] generated by monodromy operators, and let Mon2be its image in OH2(S[n],ℤ). We prove that Mon2is the subgroup generated by reflections with respect to +2 and -2 classes (Theorem 1.2). Thus Mon2does not surject onto OH2(S[n],ℤ)/(±1), when n - 1 is not a prime power.As a consequence, we get counterexamples to a version of the weight 2 Torelli question for hyperKähler varieties X deformation equivalent to S[n]. The weight 2 Hodge structure on H2(X,ℤ) does not determine the bimeromorphic class of X, whenever n - 1 is not a prime power (the first case being n = 7). There are at least 2ρ(n - 1) - 1distinct bimeromorphic classes of X with a given generic weight 2 Hodge structure, where ρ(n - 1) is the Euler number of n - 1.The second main result states, that if a monodromy operator acts as the identity on H2(S[n],ℤ), then it acts as the identity on Hk(S[n],ℤ), 0 ≤ k ≤ n + 2 (Theorem 1.5). We conclude the injectivity of the restriction homomorphism Mon → Mon2, if n ≡ 0 or n ≡ 1 modulo 4 (Corollary 1.6).

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34

Owens, Bryson, Seamus Somerstep, and Renzo Cavalieri. "Boundary expression for Chern classes of the Hodge bundle on spaces of cyclic covers." Involve, a Journal of Mathematics 14, no. 4 (October 23, 2021): 571–94. http://dx.doi.org/10.2140/involve.2021.14.571.

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35

Korotkin, Dmitry, and Peter Zograf. "Tau functions, Hodge classes, and discriminant loci on moduli spaces of Hitchin’s spectral covers." Journal of Mathematical Physics 59, no. 9 (September 2018): 091412. http://dx.doi.org/10.1063/1.5038650.

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36

Polishchuk, Alexander. "Homogeneity of cohomology classes associated with Koszul matrix factorizations." Compositio Mathematica 152, no. 10 (July 20, 2016): 2071–112. http://dx.doi.org/10.1112/s0010437x16007557.

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In this work we prove the so-called dimension property for the cohomological field theory associated with a homogeneous polynomial $W$ with an isolated singularity, in the algebraic framework of [A. Polishchuk and A. Vaintrob, Matrix factorizations and cohomological field theories, J. Reine Angew. Math. 714 (2016), 1–122]. This amounts to showing that some cohomology classes on the Deligne–Mumford moduli spaces of stable curves, constructed using Fourier–Mukai-type functors associated with matrix factorizations, live in prescribed dimension. The proof is based on a homogeneity result established in [A. Polishchuk and A. Vaintrob, Algebraic construction of Witten’s top Chern class, in Advances in algebraic geometry motivated by physics (Lowell, MA, 2000) (American Mathematical Society, Providence, RI, 2001), 229–249] for certain characteristic classes of Koszul matrix factorizations of $0$. To reduce to this result, we use the theory of Fourier–Mukai-type functors involving matrix factorizations and the natural rational lattices in the relevant Hochschild homology spaces, as well as a version of Hodge–Riemann bilinear relations for Hochschild homology of matrix factorizations. Our approach also gives a proof of the dimension property for the cohomological field theories associated with some quasihomogeneous polynomials with an isolated singularity.

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37

Othman, Hala B., Rania Mohamed Abdel Halim, Hoda Ezz El-arab Abdul-Wahab, Hossam Abol Atta, and Omyma Shaaban. "Pseudomonas aeruginosa - Modified Hodge Test (PAE-MHT) and ChromID Carba Agar for Detection of Carbapenemase Producing Pseudomonas Aeruginosa Recovered from Clinical Specimens." Open Access Macedonian Journal of Medical Sciences 6, no. 12 (November 25, 2018): 2283–89. http://dx.doi.org/10.3889/oamjms.2018.414.

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AIMS: This study aims to evaluate the ability of ChromID Carba agar, and Pseudomonas aeruginosa modified Hodge test (PAE-MHT) for detection of carbapenemase-producing P. aeruginosa and to determine the associated carbapenemase gene classes by PCR. METHODS: One hundred Carbapenem-resistant P. aeruginosa (CRPA) isolates were tested for: i) carbapenemases production by ChromID carba agar, Modified Hodge test (MHT) and (PAE-MHT) and ii) detection of some carbapenemase genes by PCR. RESULTS: All (100%) of the isolates showed growth on ChromID Carba agar with 100% sensitivity. Using MHT, 54% of isolates were positive, 3% were indeterminate, and 43% were negative, demonstrating 58.9% sensitivity and 80% specificity. On performing PAE-MHT, 91% of the strains were positive, 3% were intermediate, and 6% were negative, demonstrating 97.9% sensitivity and 80% specificity. The most prevalent gene was blaKPC (81%), followed by blaVIM (74%); blaIMP was detected in only one isolate, and blaOXA-48 in 34% of the isolates. CONCLUSIONS: We conclude that PAE-MHT and ChromID Carba are sensitive, specific, simple and cost-effective screening tests for detection of CRPA isolates compared to the traditional MHT.

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38

Banagl, Markus. "Topological and Hodge L-classes of singular covering spaces and varieties with trivial canonical class." Geometriae Dedicata 199, no. 1 (March 21, 2018): 189–224. http://dx.doi.org/10.1007/s10711-018-0345-2.

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39

Enciso, Alberto, and Niky Kamran. "Green’s Function for the Hodge Laplacian on Some Classes of Riemannian and Lorentzian Symmetric Spaces." Communications in Mathematical Physics 290, no. 1 (May 22, 2009): 105–27. http://dx.doi.org/10.1007/s00220-009-0826-0.

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40

Chappell, Isaac, S. James Gates, and T. Hübsch. "Adinkra (in)equivalence from Coxeter group representations: A case study." International Journal of Modern Physics A 29, no. 06 (March 4, 2014): 1450029. http://dx.doi.org/10.1142/s0217751x14500298.

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Using a Mathematica TM code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4×4 matrices, which in sets of four, provide representations of the 𝒢ℛ(4, 4) algebra, closely related to the 𝒩 = 1 (simple) supersymmetry algebra in four-dimensional space–time. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S4 to define distinct representations of higher-dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these 𝒢ℛ(4, 4) representations into three suggestive classes.

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BENE, ALEX JAMES. "Relations in the tautological ring derived from combinatorial classes and hyperelliptic fatgraphs." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 2 (March 2008): 369–95. http://dx.doi.org/10.1017/s0305004107000849.

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AbstractA closed formula is obtained for the integral$\int_{\Hgbs^1}\kappa_{1}\psi^{2g-2}$of tautological classes over the locus of hyperelliptic Weier points in the moduli space of curves. As a corollary, a relation between Hodge integrals is obtained.The calculation utilizes the homeomorphism between the moduli space of curves$\M_{g,1}$and the combinatorial moduli space$\Mc_{g,1}$, a PL-orbifold whose cells are enumerated by fatgraphs. This cell decomposition can be used to naturally construct combinatorial PL-cycles$W_a\subset\Mc_{g,1}$whose homology classes are essentially the Poin duals of the Mumford–Morita–Miller classes κa. In this paper we construct another PL-cycle$\Hgc \subset \Mc_{g,1}$representing the locus of hyperelliptic Weier points and explicitly describe the chain level intersection of this cycle withW1. Using this description of$\Hgc\cap W_1$, the duality between Witten cyclesWaand the κaclasses, and the Kontsevich--Penner method of integration, scheme of integrating ε classes, the integral$\int_{\Hgbs^1}\kappa_{1}\psi^{2g-2}$is reduced to a weighted sum over graphs and is evaluated by the enumeration of trees.

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PAK, HONG KYUNG. "TRANSVERSAL HARMONIC THEORY FOR TRANSVERSALLY SYMPLECTIC FLOWS." Journal of the Australian Mathematical Society 84, no. 2 (April 2008): 233–45. http://dx.doi.org/10.1017/s1446788708000190.

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AbstractWe develop the transversal harmonic theory for a transversally symplectic flow on a manifold and establish the transversal hard Lefschetz theorem. Our main results extend the cases for a contact manifold (H. Kitahara and H. K. Pak, ‘A note on harmonic forms on a compact manifold’, Kyungpook Math. J.43 (2003), 1–10) and for an almost cosymplectic manifold (R. Ibanez, ‘Harmonic cohomology classes of almost cosymplectic manifolds’, Michigan Math. J.44 (1997), 183–199). For the point foliation these are the results obtained by Brylinski (‘A differential complex for Poisson manifold’, J. Differential Geom.28 (1988), 93–114), Haller (‘Harmonic cohomology of symplectic manifolds’, Adv. Math.180 (2003), 87–103), Mathieu (‘Harmonic cohomology classes of symplectic manifolds’, Comment. Math. Helv.70 (1995), 1–9) and Yan (‘Hodge structure on symplectic manifolds’, Adv. Math.120 (1996), 143–154).

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da Silva, Genival, Matt Kerr, and Gregory Pearlstein. "Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising From Mirror Symmetry and Middle Convolution." Canadian Journal of Mathematics 68, no. 2 (April 1, 2016): 280–308. http://dx.doi.org/10.4153/cjm-2015-020-4.

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AbstractWe collect evidence in support of a conjecture of Griffiths, Green, and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degenerations over a number field. After briefly summarizing how a result of Iritani implies this conjecture for a collection of hypergeometric Calabi–Yau threefold examples studied by Doran and Morgan, the authors investigate a sequence of (non-hypergeometric) examples in dimensions 1 ≤ d ≤ 6 arising from Katz's theory of the middle convolution. A crucial role is played by the Mumford-Tate group (which is G2) of the family of 6-folds, and the theory of boundary components of Mumford–Tate domains.

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Tian, Zhiyu, and Hong R. Zong. "One-cycles on rationally connected varieties." Compositio Mathematica 150, no. 3 (March 2014): 396–408. http://dx.doi.org/10.1112/s0010437x13007549.

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AbstractWe prove that every curve on a separably rationally connected variety is rationally equivalent to a (non-effective) integral sum of rational curves. That is, the Chow group of 1-cycles is generated by rational curves. Applying the same technique, we also show that the Chow group of 1-cycles on a separably rationally connected Fano complete intersection of index at least 2 is generated by lines. As a consequence, we give a positive answer to a question of Professor Totaro about integral Hodge classes on rationally connected 3-folds. And by a result of Professor Voisin, the general case is a consequence of the Tate conjecture for surfaces over finite fields.

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Alexeev, Valery, Ron Donagi, Gavril Farkas, Elham Izadi, and Angela Ortega. "Hodge classes on the moduli space of $W(E_6)$-covers and the geometry of $\mathcal{A}_6$." Pure and Applied Mathematics Quarterly 18, no. 4 (2022): 1211–63. http://dx.doi.org/10.4310/pamq.2022.v18.n4.a1.

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46

Molcho, S., R. Pandharipande, and J. Schmitt. "The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves." Compositio Mathematica 159, no. 2 (February 2023): 306–54. http://dx.doi.org/10.1112/s0010437x22007874.

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We bound from below the complexity of the top Chern class $\lambda _g$ of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas for $\lambda _g$ in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section over the second Voronoi compactification of the moduli of principally polarized abelian varieties also cannot be expressed in terms of classes of degree 1 and 2. Along the way, we establish new cases of Pixton's conjecture for tautological relations. In the log Chow ring of the moduli space of curves, however, we prove $\lambda _g$ lies in the subalgebra generated by logarithmic boundary divisors. The proof is effective and uses Pixton's double ramification cycle formula together with a foundational study of the tautological ring defined by a normal crossings divisor. The results open the door to the search for simpler formulas for $\lambda _g$ on the moduli of curves after log blow-ups.

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Richter, Birgit, and Stephanie Ziegenhagen. "A spectral sequence for the homology of a finite algebraic delooping." Journal of K-theory 13, no. 3 (May 20, 2014): 563–99. http://dx.doi.org/10.1017/is014004016jkt264.

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AbstractIn the world of chain complexes En-algebras are the analogues of based n-fold loop spaces in the category of topological spaces. Fresse showed that operadic En-homology of an En-algebra computes the homology of an n-fold algebraic delooping. The aim of this paper is to construct two spectral sequences for calculating these homology groups and to treat some concrete classes of examples such as Hochschild cochains, graded polynomial algebras and chains on iterated loop spaces. In characteristic zero we gain an identification of the summands in Pirashvili's Hodge decomposition of higher order Hochschild homology in terms of derived functors of indecomposables of Gerstenhaber algebras and as the homology of exterior and symmetric powers of derived Kähler differentials.

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Oberdieck, Georg. "Gromov–Witten Theory of $\text{K3} \times {\mathbb{P}}^1$ and Quasi-Jacobi Forms." International Mathematics Research Notices 2019, no. 16 (November 2, 2017): 4966–5011. http://dx.doi.org/10.1093/imrn/rnx267.

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Abstract Let $S$ be a K3 surface with primitive curve class $\beta$. We solve the relative Gromov–Witten theory of $S \times {\mathbb{P}}^1$ in classes $(\beta,1)$ and $(\beta,2)$. The generating series are quasi-Jacobi forms and equal to a corresponding series of genus $0$ Gromov–Witten invariants on the Hilbert scheme of points of $S$. This proves a special case of a conjecture of Pandharipande and the author. The new geometric input of the paper is a genus bound for hyperelliptic curves on K3 surfaces proven by Ciliberto and Knutsen. By exploiting various formal properties we find that a key generating series is determined by the very first few coefficients. Let $E$ be an elliptic curve. As collorary of our computations, we prove that Gromov–Witten invariants of $S \times E$ in classes $(\beta,1)$ and $(\beta,2)$ are coefficients of the reciprocal of the Igusa cusp form. We also calculate several linear Hodge integrals on the moduli space of stable maps to a K3 surface and the Gromov–Witten invariants of an abelian threefold in classes of type $(1,1,d)$.

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Jain, Pooja, and Naveen Saxena. "Study on Phenotypic Detection of Carbapenemase Producing Enterobacteriaceae in MBS Hospital, Kota." Journal of Evolution of Medical and Dental Sciences 10, no. 29 (July 19, 2021): 2181–85. http://dx.doi.org/10.14260/jemds/2021/446.

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BACKGROUND The Carbapenemase Resistant Enterobacteriaceae (CRE) are associated with high rates of morbidity and mortality particularly amongst critically ill patients. Hence rapid laboratory detection of CRE hospitalized patients is highly desirable. The vast majority of carbapenemases belong to three of the four known classes of beta lactamases namely Ambler class A, Ambler class B metallobetalactamases (MBL) and Ambler class Doxacillinases (OXAs). The purpose of this study was to determine the prevalence of carbapenemases producing Enterobacteriaceae in clinical isolates in MBS hospital, Kota. METHODS This study was conducted in the Department of Microbiology at MBS Hospital, Kota from June 2020 to December 2020. 68 non repeat isolates (MDR) that were resistant to imipenem (10 mg) according to CLSI breakpoint were included in the present study. RESULTS Out of 68 imipenem resistant Enterobacteriaceae, 52 were carbapenemase producing as detected by Modified Hodge Test. As per our study, the prevalence of carbapenemase producing Enterobacteriaceae was 20.8%. Most commonly seen in K. pneumoniae isolated from urine and swab of critically ill and debilitated patients of surgical ward. CONCLUSIONS Curbing irrational usage of antimicrobials in India is urgently required. Thus, aggressive infection control efforts have been effective at decreasing rates of infections with KPC-producing bacteria in intensive care units and long-term acute care hospitals. Bundled interventions including enhanced environmental cleaning, active surveillance culturing and contact precautions, as well as antimicrobial stewardship are important in controlling KPC-producing bacteria. KEY WORDS Multi Drug Resistance Enterobacteriaceae (MDRE), Klebsiella Producing Carbapenemase (KPC), Carbapenem Resistant Enterobacteriaceae (CRE), Metallo Beta Lactamase (MBL), Modified Hodge Test (MHT)

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Tardini, Nicoletta, and Adriano Tomassini. "On the cohomology of almost-complex and symplectic manifolds and proper surjective maps." International Journal of Mathematics 27, no. 12 (November 2016): 1650103. http://dx.doi.org/10.1142/s0129167x16501032.

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Let [Formula: see text] be an almost-complex manifold. In [Comparing tamed and compatible symplectic cones and cohomological properties of almost-complex manifolds, Comm. Anal. Geom. 17 (2009) 651–683], Li and Zhang introduce [Formula: see text] as the cohomology subgroups of the [Formula: see text]th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds, we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology groups introduced in [Cohomology and Hodge Theory on Symplectic manifolds: I, J. Differ. Geom. 91(3) (2012) 383–416] by Tseng and Yau and a new characterization of the hard Lefschetz condition in dimension [Formula: see text] is provided.

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